On sums of subsets of Chen primes

TL;DR

This paper proves that subsets of Chen primes with positive density have sumsets with positive upper density, providing a quantitative lower bound depending on the subset's density.

Contribution

It establishes a new lower bound on the density of sumsets of subsets of Chen primes, advancing understanding of additive properties of Chen primes.

Findings

Sumsets of dense subsets of Chen primes have positive upper density.

Quantitative lower bounds depend on the subset's initial density.

Results extend additive number theory to Chen primes.

Abstract

In this paper we show that if $A$ is a subset of Chen primes with positive relative density $\alpha$, then $A+A$ must have positive upper density at least $c\alpha e^{-c^\prime\log(1/\alpha)^{2/3}(\log\log(1/\alpha))^{1/3}}$ in the natural numbers.